The rise of the gilets jaunes protest movement requires governments to prove that ordinary people and corporate elites are "in this together" in shouldering the costs of fighting climate change, a senior EU figure has said.

Frans Timmermans, the European commission's vice-president, said the movement, first triggered by a proposed rise in fuel tax in France, highlighted the need to share the burden.

He was also critical of people and groups who condemned attempts by the EU and national governments to encourage changes such as dropping single-use plastics or driving cars with lower emissions.

"This is the game of those who deny climate change or who deny the need for sustainability," he said. "They say: 'They are going to take everything away from us. They are going to take our cars away from us, they are going to take our steaks from us, they are going to take all the things that make life nice away from us. So let's not go there.'

"It is a false contradiction. If we put our policies in the right order, we have a sustainable society without lowering but even increasing our levels of wellbeing. Is wellbeing only economic growth? Only salaries? Or is wellbeing also being able to breathe clean air and drink clean water?"

Speaking before the publication on Wednesday of a "reflections paper" on the EU's next steps in changing the way Europeans live and work in order to protect the environment, Timmermans said the challenge was to bring about reform in a way that was equitable.

"The most important thing the gilets jaunes and others ask themselves is: is this fair, are people taking a fair share of the burden or are [the elites] unburdening all that on us? If you create the impression, rightly or wrongly, that this is just a burden on citizens unloaded by companies that don't do anything, then people will just block it," he said.

"Politically speaking, one of the most important tasks will be to show that this is something we are doing together in an equitable way, a fair way."

On Monday a second French gilets jaunes leader announced she was founding a political party. Its programme calls for removing privileges from elected representatives, developing "charity houses" paid for by donations from chief executives, a reduction in VAT on essential products and higher taxes for higher earners.

Timmermans said there were calls for the EU and member states to slow down in making major societal changes in favour of sustainability, but he warned: "The time is now."